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Size-Dependent Ultrafast MagnetizationDynamics in Iron Oxide (Fe3O4)Nanocrystals

Chih-Hao Hsia, Tai-Yen Chen, and Dong Hee Son*

Department of Chemistry, Texas A&M UniVersity, College Station, Texas 77842

Received November 6, 2007

ABSTRACT

Optically induced ultrafast demagnetization and its recovery in superparamagnetic colloidal iron oxide (Fe3O4) nanocrystals have been investigated

via time-resolved Faraday rotation measurements. Optical excitation with near-infrared laser pulse resulted in ultrafast demagnetization in

100 fs via the destruction of ferrimagnetic ordering. The degree of demagnetization increased with the excitation density, and the complete

demagnetization reached at

10% excitation density. The magnetization recovered on two time scales, several picoseconds and hundreds ofpicoseconds, which can be associated with the initial reestablishment of the ferrimagnetic ordering and the electronic relaxation back to the

ground state, respectively. The amplitude of the slower recovery component increased with the size of the nanocrystals, suggesting the

size-dependent ferrimagnetic ordering throughout the volume of the nanocrystal.

Ultrafast dynamics of the magnetization in magnetic materi-

als attracted a great deal of attention in recent years. 1,2 In

particular, modification of the magnetization on subpico-

second time scales using femtosecond optical pulses in ferro-

and antiferromagnetic materials has been the subject of

heated debates and active investigations.3-8 Because the

ultrashort optical excitation could manipulate the magnetiza-

tion on the time scales much faster than the typical spin-

lattice relaxation time (>100 ps), a significant effort has beenmade to understand the microscopic mechanism. During the

past decade, various mechanisms including both thermal and

nonthermal pathways were proposed to explain the optically

induced ultrafast demagnetization, magnetization, and spin

switching.9-11

From a practical point of view, the ability to control the

ultrafast magnetization is very important in applications such

as spintronics and magnetic data storage devices.12,13 Due

to the continuing demand for higher-speed and larger-

capacity devices, ultrafast magnetization dynamics in na-

nometer scale magnetic structures also gained much atten-

tion.14 Earlier efforts to investigate the ultrafast dynamicsof the magnetization in magnetic nanostructures mainly

focused on thin film structures with one-dimensional spatial

confinement or mesoscopic structures. On the other hand,

magnetic structures with three-dimensional spatial confine-

ment received much less attention,15,16 while the finite-size

effect in nanometer length scale could be more systematically

investigated. In this respect, colloidal magnetic nanocrystals

are very useful for investigating the ultrafast dynamics of

the magnetization in three-dimensionally confined magnetic

structures. The merits of colloidal nanocrystals in the study

of finite-size effect on various ultrafast dynamic processes

were previously well demonstrated in semiconductors nano-

crystals,17,18 where the methods of size and shape control

are highly developed.

In this letter, we report the femtosecond time-resolvedstudies on the optically induced ultrafast magnetization

dynamics in size-controlled superparamagnetic Fe3O4 nano-

crystals as a model system for the three-dimensionally

confined magnetic nanostructures. Linearly polarized femto-

second optical pulses at 780 nm excited the weak absorption

originating from the intervalence charge-transfer transition

between Fe3+ and Fe2+ ions. The excitation resulted in an

instantaneous decrease of Faraday rotation, indicating ultra-

fast photoinduced demagnetization. The Faraday rotation

recovered on multiple time scales ranging from a few to

hundreds of picoseconds. Here, we investigated how the

dynamics of the ultrafast demagnetization and its recovery

are affected by the density of the optical excitation and the

size of the nanocrystals.

Spherical Fe3O4 nanocrystals of three different sizes (4.5,

7.5, and 10 nm in diameter) were synthesized following the

previously reported procedure.19 Fe3O4 nanocrystals were

suspended in cyclohexane for all the measurements of this

study. While bulk Fe3O4 is ferrimagnetic, nanocrystals in

these size ranges are superparamagnetic at room tempera-

ture.20 Figure 1,panels a and b, shows the typical optical

absorption spectrum and transmission electron microscopy* To whom correspondence should be addressed. E-mail: dhson@

mail.chem.tamu.edu. Phone: 979-458-2990.

NANO

LETTERS

2008Vol. 8, No. 2

571-576

10.1021/nl072899p CCC: $40.75 2008 American Chemical SocietyPublished on Web 01/29/2008


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(TEM) image of Fe3O4 nanocrystals, respectively. The visible

absorption is primarily due to the mixture of the ligand field

transition and charge-transfer transition, while near-infrared

absorption is assigned to the intervalence charge-transfer

transition between the metal ions.21 The excitation fluence

was varied in the range of 15-61 mJ/cm2 resulting in thecorresponding average excitation density in the range of

3-12%. The approximate average excitation density wasestimated from the concentration of the nanocrystals and the

absorbed excitation pulse energy. The concentration of

nanocrystals was kept low to maintain the average interpar-ticle distance much larger than the size of the nanocrystal

(e.g., factor of 10). Dipolar interaction between the

nanocrystals is insignificant at these concentrations and

should not affect the dynamics of the magnetization.22

Time-dependent magnetization of the photoexcited Fe3O4nanocrystals was monitored by time-resolved Faraday rota-

tion measurements. Faraday rotation is proportional to

MB (t)kB, where MB (t) and kB are the magnetization vector ofthe nanocrystal and wavevector of the probe light, respec-

tively.23 Due to the high temporal resolution, time-resolved

Faraday rotation and the related technique of magneto-optic

Kerr effect have been widely utilized in the study of the

ultrafast magnetic responses.3,11,24-26 A schematic diagram

of the experimental setup is shown in Figure 2. Linearly

polarized pump pulses (780 nm, 60 fs, 3 kHz) excited the

free-streaming jet (400 m thick) of nanocrystals at room

temperature and under the external magnetic field of 0.35

T. The sample solution was circulated as a jet form to prevent

potential sample damage and accumulated thermal effects

due to the repeated exposure of the same sample area to the

pump pulses. The linearly polarized probe pulses at 620 or

900 nm, derived from white light continuum, were used to

monitor the time-dependent Faraday rotation of the photo-

excited samples. Combination of a Wollaston prism and a

balanced photodiode pair was used to measure the Faraday

rotation, which is proportional to the output signal from the

balanced photodiode normalized to the transmitted probe

intensity, S/R, for a small rotation angle. Fractional changes

of magnetization induced by the optical excitation was

obtained by measuring S/S0, where S ) [S(pump on) -S(pump off)]/R and S0 ) S(pump off)/R, respectively. Themeasured signal S/S0 in this study reflects in principle the

complex Faraday rotation with contributions of circular

birefringence and dichroism, both of which are linear to the

magnetization.27

Figure 3 shows the representative pump-probe Faradayrotation data of 7.5 nm Fe3O4 nanocrystals under Voigt and

Faraday geometries. The probe light propagates in the

direction perpendicular and parallel to the external magnetic

field for Voigt and Faraday geometry, respectively. Underthe Voigt geometry, Faraday rotation exhibits essentially no

dynamic response except a spike near zero time delay

originating from optical Kerr effect. Under the Faraday

geometry, an immediate decrease of Faraday rotation was

observed with the subsequent recovery of the signal on two

distinct time scales. The opposite polarity of the external

magnetic field yielded signals with the opposite sign (S1and S2), because the Faraday effect is odd with respect to

the magnetic field.27 To remove any potential nonmagnetic

feature in the dynamics, the difference between S1 and S2were taken to obtain the time-dependent magnetization

throughout the measurements.

No signature of a precession of the magnetization vectorwas observed up to 3 ns of delay time for both Faraday and

Voigt geometries. The lack of precessional signature may

be due to negligible photoinduced reorientation of the

magnetization or critical damping of the precession.15,28 If

the reorientation of the magnetization can be ignored, the

fractional Faraday rotation (S/S0) can be interpreted as the

fractional changes in the amplitude of the magnetization

(M/M0) in the nanocrystals.

In Figure 4, pump-probe transient absorption (OD) andmagnetization data (M/M0) are shown together to compare

Figure 1. (a) UV-vis absorption spectrum of Fe3O4 nanocrystals.(b) TEM image of 4.5 nm Fe3O4 nanocrystals.

Figure 2. Schematic diagram of the time-resolved Faraday rotationmeasurement. The external magnetic field (B) was provided by apair of permanent magnets, whose polarity was set either parallelor perpendicular to the direction of the probe light.

Figure 3. Time-resolved Faraday rotation of Fe3O4 nanocrystals(7.5 nm). S1 and S2 were obtained under Faraday geometry withthe two opposite polarities of the external magnetic field. For thesetwo curves, the signal obtained without the external magnetic fieldwas subtracted. The red curve is obtained under Voigt geometry.

572 Nano Lett., Vol. 8, No. 2, 2008


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the electronic and magnetic responses to the ultrafast optical

excitation. For an easy comparison of the dynamics, the sign

of the transient absorption data is reversed in the figure. The

transient absorption data exhibit pump-induced absorption

in the broad range of visible and near-infrared probe

wavelengths, which decays on multiple time scales withexponential time constants of ) 20 and 200 ps. Thetime scales of the dynamics were weakly dependent on the

probe wavelengths within the range 550-900 nm, while theamplitude varied with the wavelength. (See Supporting

Information) The oscillations at early delay times are due to

the coherent acoustic phonon. On the other hand, dynamics

of magnetization exhibits noticeable differences from the

transient absorption at delay times earlier than 20 ps, while

they exhibit comparable dynamics on much slower time

scales. The initial recovery of the magnetization (M/M0)

following the ultrafast demagnetization occurs on a few

picoseconds time scale and carries a larger fraction of

recovery amplitude. This component of the dynamics isabsent in the transient absorption data. The oscillatory

features are not observable unlike in transient absorption data

indicating that the coherent lattice motion does not have a

measurable effect on M/M0 in this study. The slower

recovery component of the magnetization occurs with

exponential time constants of)200 ps, which are similarto the transient absorption data. The measured M/M0 is

independent of the probe wavelength exhibiting essentially

identical dynamics at 620 and 900 nm. (See Supporting

Information)

The immediate decrease ofM/M0 following the optical

excitation in 100 fs is assigned to the ultrafast demag-

netization by the destruction of the ferrimagnetic ordering

upon the optical excitation. Optically induced demagnetiza-

tion on subpicosecond time scale was previously observed

on the surface of many ferro- and ferrimagnetic materials,3,29

although the exact mechanism has been debated for many

years. Demagnetization by the equilibration of the laser-

heated lattice and spin system via usual spin-lattice interac-tion is unlikely because the time scale for such process

typically exceeds 100 ps. Various mechanisms of optically

induced ultrafast demagnetization were proposed such as

spin-flip electron scattering, femtosecond spin-lattice re-

laxation, spin-orbit coupling during coherent excitation,magnon excitation by fast relaxing electrons or carriers,

etc.8,9,30,31 Despite the recent progresses, understanding themicroscopic mechanisms of ultrafast demagnetization con-

tinues to be a challenge because the pathways allowing the

flow of both the energy and spin angular momentum on the

relevant time scales need to be identified.32

To obtain a deeper and more quantitative understanding

of the dynamics of the demagnetization and its recovery,

M/M0 was measured at various excitation fluences. Figure

5a shows the time-dependent M/M0 of 4.5 nm Fe3O4nanocrystals as a function of the excitation fluence. The peak

value of M/M0 negatively increases with the excitation

density and saturates near -1, that is, almost completedemagnetization, at the excitation fluence of 46 mJ/cm2

corresponding to10% excitation density as shown in Figure

5b. This suggests that each absorbed photon initially

destroyed the magnetic ordering in 10 times larger number

of metal ions for 4.5 nm Fe3O4 nanocrystals. A similar degree

of the destruction of the magnetic ordering by the optical

excitation was observed earlier in ferromagnetic chalcogenide

surfaces.29

While their relative amplitudes vary as a function of the

excitation fluence, the biphasic feature of the recovery, that

is, fast ( < 5 ps) and slow ( ) 200 ps) phases, ismaintained in the entire range of the excitation fluence of

Figure 4. Comparison of the transient absorption (-OD) andmagnetization (M/M0). The left and right panels display the samedata set in different time windows.

Figure 5. (a) Excitation fluence dependence ofM/M0 of 4.5 nmFe3O4 nanocrystals. (b) Excitation fluence dependence of theamplitudes in M/M0. Triangle: peak amplitude of M/M0.Circle: amplitude of the exponential fit for ) 200 ps recoverycomponent. Solid lines superimposed on the marks are guides toan eye.

Nano Lett., Vol. 8, No. 2, 2008 573


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this study. For ) 200 ps component, the amplitudeincreases slightly superlinearly to the excitation fluence; see

Figure 5b. Slight superlinearity is due to an additional

contribution of the multiphoton absorption, which was also

observed in the transient absorption data. (See Supporting

Information) The fact that the slow magnetization recovery

and transient absorption occur on comparable time scales

and that they exhibit similar excitation fluence dependence

suggest that slow magnetization recovery reflects the relax-

ation of the excited-state to the ground state. On the otherhand, the fast recovery component of magnetization, carrying

the larger fraction of the amplitude, does not have a

corresponding feature in the transient absorption data.

To explain the distinct biphasic recovery of the magnetiza-

tion, several possibilities can be considered. One explanation

is the unequal recovery time scales for the surface and core

magnetization of the nanocrystals. In this case, the faster and

slower recovery components could be associated with the

surface and the core, respectively. However, the difference

of the recovery time scales is too large to explain simply by

the heterogeneity of metal ion sites alone. Moreover, the

surface magnetic moments are generally considered more

disordered than core with a minor contribution to the total

magnetization at high temperatures and low external fields,

such as the present experimental condition.20 In that case,

the amplitude of the faster recovery component, 10 times

larger than that of the slower component in Figure 5b, cannot

be easily accounted for by the disordered surface magnetic

moments. The fact that the fast dynamics component is

absent in the transient absorption data also suggests that it

is not associated with the electronic relaxation back to the

ground state and has a microscopic origin different from

200 ps component. Another possible explanation may

come from the consideration of the spin-spin correlation

time of magnetic moments. Because the response of thesystem is linked to its time autocorrelation via fluctuation-dissipation theorem in the linear response regime,33 examin-

ing the decay of the spin-spin time correlation function willprovide an insight into the dynamics of the magnetization.

According to the earlier simulations on the spin-spin timecorrelation function, C(t), for various model systems, the

effective decay time constant of C(t) was estimated to be in

the range of a few to tens of picoseconds. 34,35 This is similar

to the time scale of the faster magnetization recovery

component in Figure 5a. These facts suggest that fast

recovery component ofM/M0 reflects the partial reestab-

lishment of the ferrimagnetic ordering before the relaxation

of the electrons, while ) 200 ps component reflects theadditional recovery of the magnetic ordering accompanying

the electronic relaxation.

To obtain a further insight into the magnetization dynamics

and their dependence on the size of the nanocrystals, M/

M0 was measured for Fe3O4 nanocrystals of three different

sizes. Figure 6a compares M/M0 of 4.5, 7.5, and 10 nm

Fe3O4 nanocrystals. The excitation density and the optical

density at the probe wavelength were kept nearly the same

for all three samples for this comparison. M/M0 exhibits a

strong dependence on the size of the nanocrystal, especially

for its amplitude, while the biphasic recovery is observed

for all the sizes. This is in contrast to the transient absorption

data shown in Figure 6b, which do not exhibit significant

size-dependent dynamics except at very early delay times.

For the fast recovery component of M/M0, its relative

contribution to the overall recovery dynamics becomessmaller as the size of the nanocrystal increases. On the other

hand, the amplitude of the slow recovery component

increases significantly with the size. The time scales of the

magnetization recovery exhibit a slight increase as the size

of the nanocrystal increases; 3-7 and 200-360 ps for thefast and slow recovery component, respectively.

The increase of the amplitude for the slow recovery

component of M/M0 with the size of the nanocrystals

indicates that photoexcitation has a stronger influence on the

destruction and recovery of the magnetic ordering for the

larger nanocrystals. Size-dependent lattice temperature due

to different cooling rate, which is in quasi-equilibrium with

the spin degrees of freedom, cannot explain the above size-

dependence. The temperature increase in the lattice is

estimated to be less than 100 K under the present experi-

mental condition during the first several picoseconds from

the temperature-dependent coherent acoustic phonon fre-

quency and temperature-dependent elastic moduli of typical

ferrite materials.36,37 Langevin function describing the tem-

perature and field dependence of the magnetization of

superparamagnetic particles predicts M/M0 should not be

affected by more than a few percent for 7.5 and 10 nm

nanocrystals.38,39 One way to explain this observation is by

Figure 6. Size-dependent M/M0 (a) and OD (b) of Fe3O4nanocrystals at the excitation fluence of 46 mJ/cm2. The amplitudeof slower recovery component ofM/M0 increases with the sizeof the nanocrystal while OD exhibits no strong size-dependence.

574 Nano Lett., Vol. 8, No. 2, 2008


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invoking the size-dependent magnetic ordering within the

nanocrystal. One could argue that the destruction and

recovery of the ferrimagnetic ordering by the photoexcitation

would be more pronounced if the correlation among magnetic

moments of Fe ions was stronger. In this case, the observed

size dependence ofM/M0 would indicate that the magnetic

moments have a higher degree of correlation or stronger

ordering within the nanocrystal as the size increases. In fact,

the finite-size effect on the magnetic ordering in nanocrystals

has been an important issue, together with other size-dependent properties such as the static magnetization,

magnetic phase transition temperature, and superparamag-

netic relaxation.38,40,41 However, understanding of the size-

dependent magnetic ordering is still somewhat controversial.

Many experimental studies on the magnetic ordering of the

magnetic nanocrystals employed Mossbauer spectroscopy or

X-ray magnetic circular dichroism, which measured the

average spin-canting angles. While these studies revealed

that the smaller nanocrystals exhibit the larger average spin

canting, that is, the larger average spin disorder, the

interpretation was unequivocal. It could be explained with

either the core/shell model involving the disordered surface

and the ordered core42,43 or the model assuming a morehomogeneous size-dependent ordering throughout the whole

volume.44,45

The dichotomic core/shell model is, however, incompatible

with our experimental observation of the size-dependent M/

M0. Because both M and M0 should have the size

dependence from the same origin, that is, the disordered

surface, M/M0 should not exhibit a pronounced size

dependence. The size-dependent magnetic ordering through-

out the whole volume of the nanocrystals is consistent with

the observed size-dependence ofM/M0 in this study. The

increase of the faster recovery time scale of M/M0 with

the size of the nanocrystals can also be understood in terms

of the size-dependent magnetic ordering throughout the

volume. Because we associated the faster magnetization

recovery component with the partial reestablishment of the

magnetic ordering, whose dynamics are dictated by C(t), the

longer time constant for the larger nanocrystal may reflect

the stronger spin correlation within the nanocrystal.34,35

In summary, we have investigated the ultrafast dynamics

of the demagnetization and the recovery of the magnetization

following the photoexcitation of Fe3O4 nanocrystals. The

dynamics of the slowly recovering component of M/M0were well correlated with the dynamics of electronic

relaxation, while the faster recovery component was assigned

to the partial reestablishment of the ferrimagnetic orderingbefore the electronic relaxation. The amplitude ofM/M0was strongly dependent on the size of the nanocrystals,

suggesting the size-dependent magnetic ordering within the

nanocrystal.

Acknowledgment. This work was supported by Texas

A&M University and a fund from ACS-PRF Type G (45995-

G6). We thank MIC of Texas A&M University for TEM.

Supporting Information Available: Probe wavelength

dependence ofOD, excitation fluence dependence ofOD,

and probe wavelength dependence of M/M0 of Fe3O4nanocrystals. This material is available free of charge via

the Internet at http://pubs.acs.org.

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